Problem: Simplify the following expression: $ t = \dfrac{4z - 9}{z - 2} - \dfrac{-4}{7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{4z - 9}{z - 2} \times \dfrac{7}{7} = \dfrac{28z - 63}{7z - 14} $ Multiply the second expression by $\dfrac{z - 2}{z - 2}$ $ \dfrac{-4}{7} \times \dfrac{z - 2}{z - 2} = \dfrac{-4z + 8}{7z - 14} $ Therefore $ t = \dfrac{28z - 63}{7z - 14} - \dfrac{-4z + 8}{7z - 14} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{28z - 63 - (-4z + 8) }{7z - 14} $ Distribute the negative sign: $t = \dfrac{28z - 63 + 4z - 8}{7z - 14}$ $t = \dfrac{32z - 71}{7z - 14}$